TOP50 Electricity Numericals

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                BRILLIANT COACHING



                          Electricity Numericals


1. The current passing through a room heater has been halved. What will happen to the heat produced by it?


2. An electric iron of resistance 20 ohm draws a current of 5 amperes. Calculate the heat produced in 30 seconds.


3. An electric heater of resistance 8 ohm takes a current of 15 A from the mains supply line. Calculate the rate at which heat is developed in the heater.


4. A resistance of 40 ohms and one of 60 ohms are arranged in series across 220 volt supply. Find the heat in joules produced by this combination in half a minute


5. A resistance of 25 ohm is connected to a 12 V battery. Calculate the heat energy in joules generated per minute.


6. 100 joules of heat is produced per second in a 4 ohm resistor. What is the potential difference across the resistor?


7. An electric iron is connected to the mains power supply of 220 V. When the electric iron is adjusted at minimum heating’ it consumes a power of 360 W but at ‘maximum heating’ it takes a power of 840 W. Calculate the current and resistance in each case.


8. Ten bulbs are connected in a series circuit to a power supply line. Ten identical bulbs are connected in a parallel circuit to an identical power supply line.


A. Which circuit would have the highest voltage across each bulb


B. In which circuit would the bulbs be brighter?


C. In which circuit, if one bulb blows out, all others will stop glowing?


D. Which circuit would have less current in it?


9. Calculate the cost of operating a heater of 500 W for 20 hours at the rate of Rs. 3.90 per unit.


10. Which has a greater resistance, a 100 watt bulb or a 60 watt bulb?


11. How much energy is consumed when a current of 5 amperes flows through the filament (or element) of a heater having resistance of 100 ohms for two hours? Express it in joules.


12. An electric bulb is rated at 220 V, 100 W. What is its resistance?


13. An electric bulb is connected to a 220 V power supply line. If the bulb draws a current of 0.5 A, calculate the power of the bulb.


14. In which of the following cases more electrical energy is consumed per hour?


A. A current of 1 ampere passed through a resistance of 300 ohms


B. A current of 2 amperes passed through a resistance of 100 ohms.


15. Electric kettle rated at 220 V, 2.2 kW, works for 3 hours. Find he energy consumed and the current drawn.


16. In a house two 60 W electric bulbs are lighted for 4 hours, and three 100 W bulbs for 5 hours everyday. Calculate the electric energy consumed in 30 days.


17. If the potential difference between the ends of a wire of fixed resistance is doubled, by how much does the electric power increase?


18. A bulb is rated as 250 V; 0.4 A. Find its : (i) power, and (ii) resistance.


19. For a heater rated at 4 kW and 220 V, calculate (a) the current, b) the resistance of the heater, ) the energy consumed in 2 hours, and d) the cost if 1 kWh is priced at Rs. 4.60.


20. An electric motor takes 5 amperes current from a 220 volt supply line. Calculate the power of the motor arid electrical energy consumed by it in 2 hours.


21. Which uses more energy: a 250 W TV set in 1 hour or a 1200 W Toaster in 10 minutes?


22. An electric bulb is rated as 10 W, 220 V. How many of these bulbs can be connected in parallel across the two wires of 220 V supply line if the maximum current which can be drawn is 5 A.


23. How much work is done in moving a charge of 2 coulombs from a point at 118 volts to a point at 128 volts?


24. What possible values of resultant resistance one can get by combining two resistances, one of value 2 ohm and the other 6 ohm?


25. If 3 resistances of 3 ohm each are connected in parallel, what will be their total resistance?


26. If five resistances, each of value 0.2 ohm, are connected in series, what will be the resultant resistance?


27. Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series. What is the total resistance?


28. An electric bulb of resistance 20 and a resistance wire of 4 are connected in series with a 6 V battery. Draw the circuit diagram and calculate (i)the total resistance of the circuit.(ii) Current through the circuit. (iii)Potential difference across the electric bulb.(iv)Potential difference across the resistance wire.


29. How will you connect three resistors of 2 ohm, 3 ohm and 5 ohm respectively so as to obtain a resultant resistance of 2.5 ohm? Draw the diagram to show the arrangement.


30. How will you connect three resistors of resistances 2ohm, 3 ohm and 6 ohm to obtain a total resistance of: (a) 4 ohm, and (b) 1 ohm?


31. A wire of resistance R is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R then the ratio of resultant to the original will be?


32. A copper wire has a diameter of 0.5 mm and resistivity of 1.6 x 10 m.


A. What will be the length of this wire to make its resistance 10 2ohm?


B. How much does the resistance change if the diameter is doubled?


33. An electric heater which is connected to a 220 V supply line has two resistance coils A and B of 24 resistances each. These coils can be used separately (one at a time), in series or in parallel. Calculate the current drawn when


A. Only one coil A is used.


B. Coils A and B are used in series.


C. Coils A and B are used in parallel.


34. If the length of a wire is doubled by taking more of wire, what happens to its resistance?


35. How does the resistance of a wire change when


A. Its length is tripled?


B. Its diameter is tripled?


C. Its material is changed to one whose resistivity is three times?


36. How much energy is given to each coulomb of charge passing through a 6 V battery?


37. The potential difference between the terminals of an electric iron is 240 V and the current is 5.0 A. What is the resistance of the electric iron?


38. A potential difference of 20 volts is applied across the ends of a resistance of 5 ohms. What current will flow in the resistance?


39. A resistance of 20 ohms has a current of 2 amperes flowing in it. What potential difference is there between its ends?


40. A current of 5 amperes flows through a wire whose ends are at a potential difference of 3 volts. Calculate the resistance of the wire.


41. The resistance of an electric lamp filament is 230 ohms. The lamp is switched on when the line voltage is 115 volts. What is the current in the lamp circuit?


42. What is the potential difference between the ends of a conductor of 16 ohm resistance, when a current of 1.5 A flows through it?


43. Calculate the work done in moving a charge of 4 coulombs from a point at 220 volts to another point at 230 volts.


44. What is the potential difference between the terminals of a battery if 250 joules of work is required to transfer 20 coulombs of charge from one terminal of the battery to the other?


45. How much work is done in moving a charge of 2 C across two points having a potential difference of 12 V?


46. An electric bulb draws a current of 0.25 A for 20 minutes. Calculate the amount of electric charge that flows through the circuit.


47. A radio set draws a current of 0.36 A for 15 minutes. Calculate the amount of electric charge that flows through the circuit.


48. Potential difference between two points of a wire carrying 2 ampere current is 0.1 volt. Calculate the resistance between these points.


49. A simple electric circuit has a 24 V battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wires is negligible.


50. A wire of resistance R is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R then the ratio of resultant to the original will be?



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REAL NUMBERS TOP12

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CBSE TEST PAPER-01

MATHEMATICS (Class-10)

Chapter 1. Real Numbers

1. Express 140 as a product of its prime factors. (1 mark)

2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method. (1 mark)

3. Find the LCM and HCF of 6 and 20 by the prime factorization method. (1 mark)

4. State whether13/3125 will have a terminating decimal expansion or a non-terminating

repeating decimal. (1 mark)

5. State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal. (1 mark)

6. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two

numbers. (3 marks)

7. Use Euclid’s division algorithm to find the HCF of 135 and 225 (3 marks)

8. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. (3 marks)

9. Prove that 3 is irrational. (3 marks)

10. Show that 5 – 3 is irrational. (3 marks)

11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. (3 marks)

12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? (3 marks)

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Surface Area & Volumes--3 TOP8

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BRILLIANT COACHING

Chapter : Surface Area & Volumes--3

Take p= 22/7, unless stated otherwise.

1 marks Questions

Q-1 The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having diameter of the cross-section as 0.2 cm. Find the length of the wire?

Q-2 What is the height of a cone whose base area and volume are numerically equal?

Q-3 A rectangular piece of paper of dimensions 60 cm X 88 cm is rolled to form a hollow circular cylinder of height 60 cm. What is the radius of the cylinder?

Q-4 The bottom of the glass has a hemispherical raised portion. The glass is fitted with orange juice. How much juice a person will get?

2/3 marks Questions

Q-5 The curved surface area of a cone is 550 cm2. Find the volume of the cone given that its base diameter is 14 cm.

Q-6 A square field and an equilateral triangular park have equal perimeters. If the cost of ploughingthe field at the rate of Rs. 5 per m2 is Rs. 720, find the cost of maintaining the park at the rate of Rs. 10per m2.

Q-7 An iron solid sphere of radius 3 cm is melted and recast into small spherical balls of radius 1cm each. Assuming that there is no wastage in the process, find the number of small spherical balls made from the given sphere?

Q-8 A rectangular water tank of base 11 cm X 6 cm contain water up to height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of water level to be raised in this tank?

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VOLUME & SURFACE AREA TOP 10

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BRILLIANT COACHING


MATHEMATICS (Class-10)


Chapter 13 : Surface Areas and Volumes


1. How many balls, each of radius 1 cm., can be made from a solid sphere of lead of radius 8 cm.


2. A solid metallic sphere of diameter 21 cm is melted and recasted into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed.


3. A cylindrical container is filled with ice-cream, whose radius is 6 cm and height is 15cm. The whole ice-cream is distributed to 10 children in equal cones having


hemispherical tops. If the height of the conical in equal cones having hemispherical tops. If the height of the conical portion is 4 times the radius of the base, find the radius of the ice-cream cone.


4. A spherical cannon ball, 28 cm in diameter is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone,correct to one place of decimal.


5. Water flows at the rate of 10 m per minute through a cylindrical pipe having its


diameter as 5 mm. How much time will it take to fill a conical vessel whose diameter of base is 40 cm and depth 24 cm?


6. Water is being pumped out through a circular pipe whose external diameter is 7 cm. If the flow of water is 72 cm per second, how many litres of water are being pumped out in one hour?


7. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread to a width of 5 m to form an embankment. Find the height of the embankment.


8. A vessel is in the form of hemispherical bowl, is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which water will rise in the cylinder.


9. What is the least number of solid metallic spheres of 6 cm in diameter that should be melted and recast to form a solid metal cylinder whose height is 45 cm and diameter 4cm.


10. Earth taken out of digging a circular tank of diameter 17.5 m, is spread all around the tank uniformly to a width of 4 m, to form an embankment of height 2m. Calculate the depth of the circular tank correct to two decimal places.


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TRIGONOMETRY TOP 11

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BRILLIANT COACHING

MATHEMATICS (Class-10)

Chapter : Trigonometry

(Questions 1 marks)

Q1. If θ= 45o. Find the value of sec2θ

Q2. Evaluate: cos60ocos45o-sin60osin45o.

Q3. Find the value of tan15o.tan25o.tan30otan65o.tan85o.

Q4. If θ is a positive acute angle such that sec θ = cosec60o, then find the value of 2cos2 θ -1.

Q5. Find the value of sin65o-cos25o without using tables.

Q6. If sec5A=cosec(A-36o). Find the value of A.

Q7. Find the value of 9sec2A-9tan2A.

(Questions 2/3 marks)

Q1. Prove that sin6θ+cos6θ=1-3sin2θcos2θ.

Q2. From the figure find the value of sin x and cos y.

Q3. If 5tanA-4=θ, then find the value of 5sinA-cosA/5sinA+4cosA
Q4. In ABC,



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Top 3000

Basic Knowledge

Wednesday, July 30, 2008

BASIC GENERAL KNOWLEDGE

BASIC GENERAL KNOWLEDGE
1.Red cross was founded by-J.H. Durant , Established in 1864 World red Cross day iscelebrated on May 8,The Birthday its founder J.H. Durant.
2.Sir Robert S.S Baden Powell is the founder of scouting
3.Who gave the call go back to Vedas-Dayanand
4.The construction of Qutab Minar was begun by Quatab-ud-din Aibak but it was complateed by lltutumish.
5.Who built the Sanchi Stupa- Agratala.
6.Who founded slave dynasty in 1206 A.D.- Quatab-ud-din Aibak.
7.The Capital of Tripura is Agratala.
8. The Capital of Mizoram is aizawl.
9. The Capital of Australia is –Canberra.
10.Spring tides occurs on- Full moon day as well on new moon day.
11.Tides in the oceans are caused by-Attraction of the moon.
12.Buddhism place of worship is-Pongda.
13.Jews place of worship is-Synagogue.
14.Holish book of Jews-Talmud.
15.Malguddi days written by –R.K. Naraynan
16.Das capital-Karl Marx
17.The father of Economics- Adam smith.
18.The Chipko Movement was associated with-preventing felling of trees.
19.Pashmina is a breed of -Sheep.
20.What is the meaning of Buddha –An enlightened one.
21.Which is the holy book of Parsis- Jorah
22.Parliament of U.S.A is known as- Congress
23. Parliament of Afghanistan- Shoora
24. Parliament of Russia-Duma.
25. Parliament of Japan –Diet.
26.SARS:-It Stands for Severe Acute Respiratory Syndrome. SARS is caused by viruses from the corona and paramyxo virus family.
27.New Governors of India:-
-Kailashpati Mishara – Gujrat
-Ram Parkash Gupta –Madhya Pradesh
-O.P Verma -Punjab
-V.S Kokje - Himachal Pradesh
-Nirmal Chand - Rajasthan
28.LCA(Light Combat Aircraft)is named as “Tejas”
29. Lakshva is Pilot Less target Aircraft
30.Kalpna Chawla: She was an Indian born American Astronaut. She died with other six astronauts in the Columbia shuttle crash on feb.1,2003.She embarked on her second Voyage in the United State space shuttle Columbia on Jan 16,earlier.She was an Indian born American Astronaut.She died with other six astronauts in the Columbia shuttle Columbia on jan 16,earlier.She
was one of the six astronaut crew that flew the
Columbia Flight STS-87in nov.1997 Chawla who had her schooling in Karnal (Haryana)and college education in Punjab did her Masters in Aerospase Engineering from the university of Taxes in in 1984 and Doctorate from Colorado University two year later. An avid flier, she held certified flight instructor’s license with Airplane and Gladder ratings, commercial Pilot L icense for single and multi-engine land and seaplanes
31.Jan. 9,the day Mahatma Gandhi return from South Agrica in 1915-was chosen to celebrate the Pravasi Bharatiya Divas
32.The five day 90th session of the Lndian science congress conclude in Bangalore on Jan.7,2003.The focal theme of the congress was Vision for the global Space community.
33.Sriska and Ranthambore are the reserve for lion.
34.International Criminal court was launched formally in the mid march in the Hauge . The first eighteen judges took Oath in the grand ceremony. The court has been set up to handle genocide and the Worst case of war crime or mass atrocities against civilians when no national court
is able or willing to do so.
35.Right to Education:-article 21A provides the free and compulsory education to all children of
the age of six to fourteen.
36.Freedom of information bill:- The parliament approved the “Freedom of information bill”.Now it is statutory right of the citizen to access information from the Government.
37.Right to Education :- article21A provides the free and compulsory education to all children of the age of six to fourteen
38.Freedom of information bill:- The Parliament approved the “freedom of information bill”. Now it is statutory right of the citizen to access information from the Government.
39.Minister of state for defence is prof. Chaman lal gupta
40.Ajit singh is Agriculture Minister.
41. Sapan is not a member of G-8 group.
42. APSARA is the name of the India’s first Nuclear Reactor.
43.The world environment day is celebrated on june 5.
44.Jainism:-Founded by (Rishabha)Varhamana Mahavira. He was a great 24th Triathankras (Pathfinder).Or prophet of Jainism .Mahavir was a
greast Kshtiya ,born at Kundagram (Vaishali) in bihar. He came to be known as Mahavir of jina. The conqueror of passing; his following are known as Janis. He passed away at age 72 in 462 B. C at Pavapuri, a place near modern Rajgir . Mahavira Teaching are known as the “Tri Ratna” or the three jewels of Jainisn,which lead to the attainment of salvation . They are (I) Right Knowledge and (II) Right Action .The Janis used and developed Prakrit,The language of the common people .Their religious literature was written in Ardhamagadhi.
45.Vasco da Gama landed in Calicut in 1498.
46.Ist Chinese traveler, Fahein came to India during the period of chandra Gupta-II(Vikramaditya)
47.2nd Chinese traveler Hieun Tsang came to India during the region of Harshvardhana
48.Who is the Napoleon of India –Samundra Gupta for his military exploits.
49.Harshvardhana written three books-1.Priya Darshika 2.Rattanavali 3.Naga Nanda. The official poet of harshvardhana was bana bhatt .Bana bhatta
composed harsha chirtra and kadambari
50.first battle of panipat in 1526 and founded
the Mugahal dynasty in India
51.Second battle of Panipat was fought between
Akbar and Ibrahim Lodhi at Panipat in 1556 Akbar
Defeated Himu and became the ruled of Delhi and Agra
52 Third battle of Panipat fought between Ahmed Shah Abdali of Afghanistan and Marathas in 1761.In this third battle of Panipat Marathas were completely routed by Ahmed Shah Abdali.
53.Indian National Army was founded by Subash Chander Bose in 1943 in Singapore alongwith Rasbihari Bose. The main aim of Azad Hind Fauz
was to liberation of India.
54.The Brahmo Samaj was established by Raja Ram Mohan Roy in 1828 whose leadership was later taken by Debendernath tagore and Keshub Chande Sen.
55.The Arya Samaj founded by Swami Dayananda Saraswati in 1875 attempted to reform the Hindu religion from its decadence.
56.The Ramakrishana Mission was founded by
Swami Vevekananda in 1896 .
57.Annie besant:- Founded Theosophical society started home rule league in 1916. She was the first woman president of Indian National Congress.Indian National Congress Founded by A.O.Hume in 1885. However first President of Indian national congress was W.C. Banerjee.
58.Swadeshi movement was started in 1905.
59.Gadder party was founded by lala Hardayal singh in 1913 at Francisco.
60.Home rule league founded by Annie Besant and Bal Ganga Dhar Tilak in 1916.
1916.Rowlatt Act. Passed in 1919.
61.Non-Co-Operation movement started in 1920 by Gandhi ji. This movement ended in 1922 after Chauri Chaura incident.
62.Simons commission –1928
63.Civil Disobedience movement-1930
64. “Do or die” –Mahatma Gandhi
65. “Nightingale of India”-Saorjini Naidu.
66. “Father of Indian Unrest”-Bal Ganga Dhar Tilak.
67. “Architect of India”- Pandit Nehru.
68. “
Man of Peace”-Lal Bhadur Shastri.
69. “Iron Man of India”-Sardar.
70. “jai hind” –subash chander bose
71. “Grand old man of India” –Dada Bhai Naroji

Time & Work Top 30 Questions

TRIGONOMETRY MCQ

BRILLIANTCOACHING

TRIGONOMETRY - Class 10 Maths MCQs

The line drawn from the eye of an observer to the point
in the object viewed by the observer is known as

Choose one:

	horizontal line
	vertical line
	line of sight
	transversal line

When we raise our head to look at the object, the angle
formed by the line of sight with the horizontal is known
as

Choose one:

	acute angle
	angle of elevation
	angle of depression
	right angle

Two poles are 25 m and 15 m high and the line joining
their tops makes an angle of 45

Choose one:

	5 m
	8 m
	9 m
	10 m

The angle of elevation of the top of a tower from a point 20 metres away from its base is 45

Choose one:

	10 m
	20 m
	30 m
	20 √ 3

The tops of two poles of height 20 m and 14 m are
connected by a wire. If the wire makes an angle of 30"
with the horizontal, then the length of the wire is

Choose one:

	8 m
	10 m
	12 m
	14 m

The angle of elevation of the top of a 15 m high tower at
a point 15 m away from the base of the tower is

Choose one:

	30
	60
	45
	75

When we lower our head to look at the object, the angle
formed by the line of sight with the horizontal is known as

Choose one:

	obtuse angle
	angle of elevation
	angle of depression
	acute angle

If two towers of height h] and h2 subtend angles of 60:
and 30

Choose one:

	1: 2
	1: 3
	2:1
	3:1

When a point is observed, the angle formed by the line of sight with the horizontal where the point being viewed is above the horizontal level is known as

Choose one:

	angle of elevation
	angle of depression
	angle of a triangle
	right angle

A person standing on the bank of a river find that the
angle of elevation of the top of a tower on the opposite
bank is 45

Choose one:

	breadth of the river is twice the height of the tower.
	breadth of the river is half of the height of the tower.
	breadth of the river is equal to the height of the tower.
	none of these.

POLYNOMIAL HOTS

11

                                  BRILLIANT COACHING

UNIT-2

POLYNOMIALS

It is not once nor twice but times without number that the same ideas

make their appearance in the world.

1. Find the value for K for which x

(Ans : K= - 91)

4 + 10x3 + 25x2 + 15x + K exactly divisible by x + 7.

Ans:

Since P(x) exactly divisible by g(x)

Let P(x) = x4 + 10x4 + 25x2 + 15x + K and g(x) = x + 7

\

now x + 7

r (x) = 0

3 2

4 3 2

4 3

3 4 13

10 25 15

7

x x x

x x x x K

x x

+ + −

+ + + +

+

-------------

3x

3 + 25 x2

3x

3 + 21x2

-------------------

4x

4x

------------------

-13x + K

- 13x - 91

----------------

K + 91

------------

2 + 15 x2 + 28x

\

2. If two zeros of the polynomial f(x) = x

other zeros. (Ans:7, -5)

K + 91 = 04 - 6x3 - 26x2 + 138x – 35 are 2± Ö3.Find the

Ans

Sum of Zeros = 2 + 3 + 2 - 3

= 4

Product of Zeros = ( 2+ 3 )(2 - 3 )

= 4 – 3

= 1

Quadratic polynomial is x

K= -91

12

x

x

4 3 2

: Let the two zeros are 2 + 3 and 2 - 32 – (sum) x + Product2 – 2x – 352 – 4x + 1 4 3 2

6 26 138 35

4

x x x x

x x x

− − + −

− +

-----------------

-2x

- 2x

-----------------------

-35x

-35x

------------------------

0

------------------------

3 – 27x2 + 138x3 + 8x2 – 2x2 + 140x – 352 + 140x – 35

\

(x – 7)(x + 5) = 0

x = 7, -5

3. Find the Quadratic polynomial whose sum and product of zeros are

2 1

1

x2 – 2x – 35 = 0Ö2 + 1,

+

.

Ans:

Product = 1

Q.P =

X

sum = 2 22 – (sum) x + Product

\

4. If

(

x2 – (2 2 ) x + 1a,b are the zeros of the polynomial 2x2 – 4x + 5 find the value of a) a2 + b 2 b)a - b)2.

(Ans: a) -1 , b) –6)

Ans

: p (x) = 2 x2 – 4 x + 5

a

4

2

+ b =

b

a

−

=

= 2

a b

5

2

=

c

a

=

a

2 + b2 = (a + b)2 – 2 a b

Substitute then we get,

(

a 2+ b2 = -1a - b)2 = (a + b)2 - 4 a b

Substitute, we get = (

other two Zeros are 7 and -5

13

5. If

whose zeros are a)

a - b)2 = - 6a,b are the zeros of the polynomial x2 + 8x + 6 frame a Quadratic polynomial

a

1

and

b

1

b) 1 +

a

b

, 1 +

b

a

.

(Ans: x

3

4

+

6

1

, x

3

32

+

3

32

)

2+ x2- x

Ans:

p (x) = x2 + 8 x + 6

a

a) Let two zeros are

+ b = -8 and a b = 6

a

1

and

b

1

Sum =

a

1

+

b

1

=

.

a b

a b

+

=

8

6

−

=

4

3

−

Product =

a

1

x

b

1

=

1 1

a

.b 6

=

Required Q.P is

x

4 1

3 6

2 +

x

+

b) Let two Zeros are 1+

a

b

and 1 +

b

a

sum = 1+

a

b

+1+

b

a

= 2 +

b

a

+

a

b

= 2+

ab

a

2 + b 2

= 2+

ab

(

a b ) 2ab + 2 −

after solving this problem,

We get =

3

32

Product = ( 1 +

a

b

)(1+

b

a

)

= 1+

b

a

+

a

b

+1

= 2 +

ab

a

2 + b 2

Substitute this sum,

14

We get =

3

32

Required Q.P. is x

3

32

x +

3

32

6. On dividing the polynomial 4x

quotient is x

(Ans:4 x

2 -4 - 5x3 - 39x2 - 46x – 2 by the polynomial g(x) the2 - 3x – 5 and the remainder is -5x + 8.Find the polynomial g(x).2+7x+2)

Ans:

g(x) =

( )

( ) ( )

p(x) = g (x) q (x) + r (x)

q x

p x

− r x

let p(x) = 4x

q(x) = x

now p(x) – r(x) = 4x

when

( )

( ) ( )

4 – 5x3 – 39x2 – 46x – 22 – 3x – 5 and r (x) = -5x + 84 – 5x3 – 39x2 – 41x - 10

q x

p x

− r x

= 4x

2 + 7x +2

\

7. If the squared difference of the zeros of the quadratic polynomial

equal to 144 , find the value of p. (Ans:

g(x) = 4x2 + 7x + 2x2 + px + 45 is± 18).

Ans:

Let two zeros are a and b where a > b

According given condition

(

Let p(x) = x

a - b)2 = 1442 + px + 45

a

+ b =

a

−

b

=

1

−

p

= - p

ab

=

a

c

=

1

45

= 45

now (

(

(-p)

Solving this we get p =

8. If

Quadratic polynomial having

a - b)2 = 144a + b)2 – 4 ab = 1442 – 4 (45) = 144± 18a,b are the zeros of a Quadratic polynomial such that a + b = 24, a - b = 8. Find aa and b as its zeros. (Ans: k(x2– 24x + 128))

Ans:

a+b = 24

a

-----------

2

15

- b = 8a = 32

a

2

32

= 16,

Work the same way to

So,

Q.P is x

= x

Solve this,

it is k (x

9. If

a.

=\ a = 16a+b = 24b = 82 – (sum) x + product2 – (16+8) x + 16 x 82 – 24x + 128)a & ß are the zeroes of the polynomial 2x2 4x + 5, then find the value ofa2 + ß2 b. 1/ a + 1/ ß c. (a ß)2 d. 1/a2 + 1/ß2 e. a3 + ß3

(Ans:-1,

5

4

,-6,

25

−

,-7)

4

Ans:

Let p(x) = 2x2 – 4x +5

a

+b =

a

−

b

=

2

4

= 2

ab

=

a

c

=

2

5

a)

a2+b2 = (a+b)2 - 2ab

Substitute to get =

b)

a2+b2 = -1

a

1

+

b

1

=

ab

a

+ b

substitute , then we get =

a

1

+

b

1

=

5

4

b) (

a-b)2 = (a+b)2 - 4 ab

Therefore we get, (

d)

a-b)2 = - 62

1

a

+

2

1

b

=

2 2

2

ab

a

+ b

=

2

2

5

1

−

\

2

1

a

+

2

1

b

=

25

−

e)

Substitute this,

to get,

16

10. Obtain all the zeros of the polynomial p(x) = 3x

zeroes are

4a3+b3 = (a+b)(a2+b2 - ab)a3+b3 = -74 15x3 + 17x2 +5x 6 if two 1/3 and 1/3. (Ans:3,2)

11.

algorithm.

a. deg p(x) = deg q(x) b. deg q(x) = deg r(x) c. deg q(x) =

Give examples of polynomials p(x), g(x), q(x) and r(x) which satisfy the division0.

12. If the ratios of the polynomial ax

3abc+a

3+3bx2+3cx+d are in AP, Prove that 2b3-2d=0

Ans:

but zero are in AP

let

sum =

Let p(x) = ax3 + 3bx2 + 3cx + d and a , b , r are their three Zerosa = m – n , b = m, r = m + na+b+ r =

a

−

b

substitute this sum , to get = m=

a

−

b

Now taking two zeros as sum

ab +b r +ar =

a

c

(m-n)m + m(m+n) + (m + n)(m – n) =

a

3

c

Solve this problem , then we get

2

2

3 3

a

b

− ac

= n

2

Product

ab r =

a

d

(m-n)m (m+n) =

a

−

d

(m

2 –n2)m =

a

−

d

[(

a

−

b

)

3 3

2 – ( )

2

2

a

b

− ac

] (

a

−

b

) =

a

−

d

Simplifying we get

2b

17

13. Find the number of zeros of the polynomial from the graph given.

(Ans:1)

14. If one zero of the polynomial 3x

zeros and the value of k (Ans k= 2/3)

3 – 3abc + a2 d = 02 - 8x +2k+1 is seven times the other, find the

Self Practice

14. If (n-k) is a factor of the polynomials

k = n +

x2+px+q & x2 + m x+n. Prove that

m p

n q

−

−

Ans :

since (n – k) is a factor of x2 + px + q

\

And (n – k)

Solve this problem by yourself,

(n – k)2 + p(n- k) + q = 02 + m(n – k) + n = 0

\

k = n +

m p

n q

−

−

SELF PRACTICE

16. If 2, ½ are the zeros of px

17. If m, n are zeroes of ax

(Ans: a=1/2 ,c=5)

18. What must be subtracted from 8x

polynomial is exactly divisible by 4x

19. What must be added to the polynomial p(x)= x

resulting polynomial is exactly divisible by x2+5x+r, prove that p= r.2-5x+c, find the value of a and c if m + n = m.n=104 + 14x3 – 2x2 + 7x –8 so that the resulting2+3x-2. (Ans: 14x – 10)4 + 2x3 – 2x2 + x –1 so that the2+2x-3. (Ans: x-2)